For a worked example during his atomic spectrum lecture and module, the question asked us to calculate frequency of light emitted by a hydrogen atom when an electron makes a transition from the 4th to 2nd principal quantum level. I understand that we first need to calculate the energies of both the 4th and 2nd levels in order to find the difference in energy (which is negative). But next, when using the frequency = energy/Planck's constant equation, why do we make the energy positive? Is frequency always supposed to be a positive value?

So we make the energy positive because the change in energy of the electron is equal to the energy of the light emitted. When an electron is dropped from a higher energy level to a lower energy level, the electron loses some energy (this is delta E, or change in E). This energy is lost because it's emitted as light. So the change in E is equal to the E of the light emitted. So when plugging in E into the E=hv equation (in Professor Lavelle's example), E would be positive because this is simply the energy of the light emitted.

The values are going to be positive because the light emitted is equal to the energy "lost" by the electron when it dropped levels. Although that may be seen as negative and confusing, it balances out.